1
Tables and ordered pairs from an equation
Discover Mathematics P6: Term 1, Unit 5, Lessons 3–4
GoalUse an equation to make a table of values and ordered pairs, and find missing values.
New words
ordered pair · two numbers (x, y) in this order: input first, output secondtable of values · a list of inputs with the outputs they givemissing value · a number in a table that we must find
Explanation
One relationship can be shown in several ways: in words, as an equation, as a table and as ordered pairs. For y = 4x, choose inputs x = 1, 2, 3 and work out y = 4, 8, 12. Each input with its output makes an ordered pair, written with the input first: (1, 4), (2, 8), (3, 12). To find a missing value, use the equation: if y = 28, then 4x = 28, so x = 7. We can also describe the change: each time x goes up by 1, y goes up by 4.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y = 4x | 0 | 4 | 8 | 12 | 16 |
| pair (x, y) | (0, 0) | (1, 4) | (2, 8) | (3, 12) | (4, 16) |
Worked examples
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 4 | 8 | 12 | 16 | 20 |
| t | 2 | ? | 6 |
|---|---|---|---|
| p = 15t | 30 | 60 | ? |
| n | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| c = 3n + 2 | 2 | 5 | 8 | 11 |
Class activity
Table race. A grown-up writes an equation like y = 6x. You have one minute to complete a table for x = 1 to 8 and to write all the ordered pairs. Check with a calculator or by counting in 6s. Then make a table with one missing value for the grown-up to find.
Practice
1
Complete the table for y = 6x with x = 1, 2, 3, 4.
y = 6, 12, 18, 24.
2
Write the ordered pairs of y = x + 3 for x = 1, 2, 3.
(1, 4), (2, 5) and (3, 6).
3
In y = 7x, find x when y = 35.
7x = 35, so x = 5.
4
A cyclist rides d = 50t km in t hours. Find d for 3 hours and t for 200 km.
d = 50 × 3 = 150 km. For 200 km: 50t = 200, so t = 4 hours.
5
In y = 9x, how does y change when x goes up by 1?
y goes up by 9.